There are many ways to attempt to minimize costs involved with inventory replenishment. The inventory can contain any number and type of products or items, e.g., clothes, spare parts, grades of oil, office supplies, etc. When attempting to determine an appropriate inventory policy various cost components can be considered, for example, ordering costs, holding costs, backlog costs, etc. Also, when determining an inventory control policy various assumptions can be used, for example, that demand for inventory items is independent, or that there will be one-for-one item replenishment upon ordering.
One specific type of inventory replenishment problem is referred to as the stochastic joint replenishment problem (SJRP). The SJRP is directed to determining a method of ordering some set of items that are subject to random (stochastic) demands in such a way as to minimize the joint costs of ordering, holding inventory, and backlogging demand. The term “joint” is used herein to indicate that costs are coupled and economies of scale arise when multiple items are simultaneously ordered.
While various heuristic policies have been proposed for the SJRP (e.g., can-order, periodic review, Q(s,S)), these policies can be arbitrarily sub-optimal. Methods for determining optimal policies such as policy and value iteration can become impractical when more than 7 items are considered, in part due to the need for excessive computational power. There has been significant research to determine heuristic policies that guarantee a close-to-optimal policy in closely related problems such as power-of-two policies for deterministic joint replenishment and cost balancing policies for single-item and multi-echelon replenishment. However it is not obvious to extend these heuristics to the SJRP. Thus, there is a need to overcome these and other problems with the prior art and to provide an inventory policy that can more optimally minimize costs for the SJRP.